Electronic Band Structure Study of the Anomalous Electrical and Superconducting Properties of Hexagonal Alkali Tungsten Bronzes A x WO 3 (A ) K, Rb, Cs) Kwang-Soon Lee, † Dong-Kyun Seo, ‡ and Myung-Hwan Whangbo* ,‡ Contribution from the Departments of Chemistry, The Catholic UniVersity of Korea, Puchon, Kyonggi-Do, South Korea 422-743, and North Carolina State UniVersity, Raleigh, North Carolina 27695-8204 ReceiVed December 30, 1996 X Abstract: The electrical and superconducting properties of hexagonal alkali tungsten bronzes A x WO 3 (A ) K, Rb, Cs) were examined by calculating the electronic band structure of a representative hexagonal tungsten bronze and analyzing reported crystal structures of A x WO 3 (A ) K, Rb, Cs). These bronzes possess one-dimensional (1D) and three-dimensional Fermi surfaces. The metal-to-semiconductor-to-metal transitions and superlattice reflections in K x WO 3 and Rb x WO 3 are explained by a charge density wave (CDW) associated with the 1D Fermi surface. There occurs a maximum in the plots of the CDW onset temperature T B versus x for K x WO 3 and Rb x WO 3 . The presence of this maximum and the absence of a CDW in Cs x WO 3 reflect the balance of two opposing energy factors, the electronic instability and lattice stiffness, in forming a CDW. The dependence of the superconducting transition temperature T C on x suggests that a CDW transition removes lattice phonons conducive for superconductivity. 1. Introduction The structures and physical properties of hexagonal alkali tungsten bronzes A x WO 3 (A ) K, Rb, Cs; O < x < 1 / 3 ) have been the subject of numerous studies. 1-23 These bronzes have a three-dimensional (3D) WO 3 lattice made up of corner-sharing WO 6 octahedra, and the alkali cations A + are located in the hexagonal tunnels of the lattice. 1-14 Thallium and indium tungsten bronzes, Tl 0.30 WO 3 and In 0.30 WO 3 , 5,24 are isostructural with the hexagonal alkali tungsten bronzes, but other alkali tungsten bronzes Li x WO 3 and Na x WO 3 25 belong to a different structural type and are isostructural with cubic hydrogen tungsten bronze D x WO 3 . 26 The maximum x value of 1 / 3 in A x WO 3 (A ) K, Rb, Cs) results when all the alkali atom sites in the hexagonal tunnels are occupied. The t 2g -block bands of the WO 3 lattice become partially filled by the electrons donated from the alkali atoms, which renders metallic properties to A x WO 3 (A ) K, Rb, Cs). The hexagonal tungsten bronzes exhibit puzzling electrical and superconducting properties. 15-23 K x WO 3 and Rb x WO 3 show a metal-to-semiconductor-to-metal phase transition (Figure 1) in their electrical resistivity along the crystallographic c-direction, 18,20 but not along the directions perpendicular to the c-direction. 20,21 The metal-to-semiconductor phase transition in A x WO 3 (A ) K, Rb) reduces the density of the carriers responsible for the electrical conduction along the c-direction, † The Catholic University of Korea. ‡ North Carolina State University. X Abstract published in AdVance ACS Abstracts, April 15, 1997. (1) Magneli, A. Acta Chem. Scand. 1953, 7, 315. (2) Galasso, F.; Darby, W. J. Phys. Chem. 1964, 68, 1253. (3) Goodman, P. Acta Crystallogr. 1976, B32, 3280. (4) Hussain, A.; Kihlborg, L.; Klug, A. J. Solid State Chem. 1978, 25, 189. (5) Labbe ´, Ph.; Goreaud, M.; Raveau, B.; Monier, J. C. Acta Crystallogr. 1978, B34, 1433. (6) Kihlborg, L.; Hussain, A. Mater. 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